What is Factorise using factor theorem?

In mathematics, factor theorem is used when factoring the polynomials completely. It is a theorem that links factors and zeros of the polynomial. According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number, then, (x-a) is a factor of f(x), if f(a)=0.

What do u mean by factor theorem?

Factor Theorem is a special case of Remainder Theorem. Remainder Theorem states that if polynomial ƒ(x) is divided by a linear binomial of the for (x – a) then the remainder will be ƒ(a). Factor Theorem states that if ƒ(a) = 0 in this case, then the binomial (x – a) is a factor of polynomial ƒ(x).

What is factor theorem with example?

Answer: An example of factor theorem can be the factorization of 6×2 + 17x + 5 by splitting the middle term. In this example, one can find two numbers, ‘p’ and ‘q’ in a way such that, p + q = 17 and pq = 6 x 5 = 30. After that one can get the factors.

What is factor theorem Class 9 definition?

Factor Theorem. Factor Theorem. x – a is a factor of the polynomial p(x), if p(a) = 0. Also, if x – a is a factor of p(x), then p(a) = 0, where a is any real number. This is an extension to remainder theorem where remainder is 0, i.e. p(a) = 0.

What is the use of factor theorem?

Factor theorem is usually used to factor and find the roots of polynomials. A root or zero is where the polynomial is equal to zero. Therefore, the theorem simply states that when f(k) = 0, then (x – k) is a factor of f(x).

What is the difference between factor theorem and Remainder Theorem?

The remainder theorem tells us that for any polynomial f(x) , if you divide it by the binomial x−a , the remainder is equal to the value of f(a) . The factor theorem tells us that if a is a zero of a polynomial f(x) , then (x−a) is a factor of f(x) , and vice-versa.

How do you Factorise factor theorem Class 9?

Factorization Of Polynomials Using Factor Theorem

1. Obtain the polynomial p(x).
2. Obtain the constant term in p(x) and find its all possible factors.
3. Take one of the factors, say a and replace x by it in the given polynomial.
4. Obtain the factors equal in no. to the degree of polynomial.
5. Write p(x) = k (x–a) (x–b) (x–c) …..

What is the factor theorem simple?

How do you use the factor theorem?

In practice, the Factor Theorem is used when factoring polynomials “completely”. Rather than trying various factors by using long division, you will use synthetic division and the Factor Theorem. Any time you divide by a number (being a potential root of the polynomial) and get a zero remainder in…

What is the remainder factor theorem?

The remainder factor theorem is actually two theorems that relate the roots of a polynomial with its linear factors. The theorem is often used to help factorize polynomials without the use of long division.

What is the definition of factor theorem?

Factor theorem. In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem.

What is the linear factorization of a polynomial?

A linear factor of a polynomial is univariate, meaning it only has one variable that affects the function. Typically, the variable will be designated as x and will correspond to movement on the x-axis. The function will also typically be labeled as y, as in y = ax+b.